JP2007259447A - Frequency estimation method, wideband frequency discriminator and radiolocalization receiver - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a frequency discriminator based on a combination of DFT operator and half-bin DFT operator, corresponding to a set of twiddle factors with frequency two times the sampling frequency. <P>SOLUTION: The frequency estimators are so selected as not to have any zero or discontinuity point. Therefore the discriminator of the invention is more stable and well behaved in an extended operating range. The discriminator of the invention, when applied to a GPS receiver, allows a safer lock to the carrier frequency, even in presence of a large initial error, and avoids the problem of false locks. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for estimating the frequency of a signal and a corresponding apparatus. The invention is particularly for the acquisition and tracking of position measurement signals such as position measurement signals, for example signals emitted from one or more GPS (satellite navigation systems) or other radio position measurement system related signals. Although the present invention relates to the use of the method and apparatus, the present invention is not limited thereto.

  Frequency estimation, particularly frequency estimation of sinusoidal signals, is an operation used in many applications.

  Here, the term frequency discriminator is used in terms of function to indicate an algorithm or mathematical operation that can be applied to a vector representing a sampling signal to estimate the fundamental frequency of the signal itself. . Similarly, the term frequency discriminator may refer to a piece of software that, for example, determines the frequency of a signal represented by a series of time samples in the context of the present invention. Also, in the following, the term frequency discriminator shall refer to a component of an electronic circuit configured or programmed to estimate the fundamental frequency of an analog or digital signal supplied to the input when referring to the device. To do.

  An example of the use of a frequency discriminator is the FLL (frequency lock loop) schematically illustrated in FIG. In this example, the input signal 43 is combined with the signal of the local oscillator 46 by the mixer 45. The differential frequency obtained as a result is applied to the frequency discriminator 47. The result of the frequency discriminator is basically proportional to the difference between the fundamental frequency of the input and the nominal frequency, and is used to drive a local oscillator in the feedback loop containing the filter 48 to tune at the same frequency as the received signal. ing.

  An important application of frequency discriminators is in the carrier tracking loop of a GPS receiver. The operation of a GPS receiver has a capture mode that searches for signals received from a normal space vehicle (SV) and a tracking mode that tracks the captured signals with respect to both carrier frequency or phase and code phase.

  The frequency of the signal received from the SV in the GPS system is basically a physical Doppler associated with some instrumental error, eg, local oscillator frequency bias and drift, and the relative speed between the SV and the receiver. In order to be affected by the shift and to keep track of the SV and to reach the position measurement, these must be measured appropriately. It is typically implemented in a GPS receiver using PLL and FLL feedback loops.

  Typically, the FLL loop is used during the acquisition phase because of its excellent noise margin. The PLL provides good tracking performance if the signal length is appropriate. The FLL fallback mode is often provided instead of a PLL to track weak signals as well as during peak fluctuations due to receiver motion.

  In many applications, frequency estimation is performed by applying a mathematical definition of the frequency at that frequency as the time derivative of the phase (

). In that case, the phase increase rate is regarded as an estimated amount of frequency as follows.

  However, this approach cannot be used in practice if the noise exceeds a certain threshold and the phase signal cannot be clearly detected.

  Another common approach is to use frequency discrimination in the time domain as described below. Unfortunately, such discriminators exhibit rather narrow lock frequency ranges and spurious zeros or discontinuities outside the lock range. When such discriminators are employed in the frequency control loop, zeros or discontinuities outside these ranges will create a stable spurious lock position outside the design lock range. The above-described phase differential discriminator based on the time domain is also affected by the same problem.

Another possible method is to extract one or more DFTs (Discrete Fourier Transforms) of the input signal. Such partial amplitudes can be combined mathematically in various ways to provide the desired frequency. However, known DFT frequency discriminators are affected by non-linearities and out-of-range zeros or discontinuities, thus limiting the upstream equipment.
Japanese Patent Laid-Open No. 10-294675

  An object of the present invention is to provide a frequency estimation method and a frequency discriminator that do not have the above-described drawbacks, and in particular, to provide a frequency discriminator that has an extended lock range and is stable within the lock range. is there.

  Another object of the present invention is to provide a frequency discriminator that does not have a spurious lock point outside the lock range.

  Still another object of the present invention is to provide a frequency control circuit with improved accuracy and a radio position measuring receiver employing the frequency control circuit.

  These objects are achieved based on the present invention using the contents described in the independent claims. Additional optional features are set forth in the dependent claims.

  The invention is better understood from the description of the exemplary embodiments illustrated in the drawings.

  For example, a well-known frequency discriminator widely used in wireless position measurement receivers is a simple “cross” discriminator represented by the following equation:

Here, I ₁ and I ₂ are real components of the complex sine wave signal at _two time points T ₁ <T ₂ , and Q ₁ and Q ₂ correspond to the same signal at the same time point T ₁ and T _2. It is an imaginary component. The observation time ΔT = T ₂ −T ₁ has a relationship between the nominal lock range and W _Cross = 1 / (2 · ΔT).

  Referring to FIG. 16, along with the discriminator output 190d according to the present invention, the response of the "cross" discriminator is represented by curve 190b. The output of the “cross” discriminator shows a zero point that works well within its locking range, but otherwise locks stably.

  FIG. 16 also illustrates other known variations of this class of discriminators, the “signDotCross” type discriminator corresponding to curve 190a as follows:

The output of the arctangent discriminator (AtanDisc) is shown by curve 190c as follows.

  Both of these discriminators show a zero or discontinuity point corresponding to a false lock point outside the operating range.

  It is known to use a discrete Fourier transform (DFT) to implement a frequency discriminator for digital signals. Conceptually, this class of discriminator is based on the principle of comparing the outputs of at least two different DFT operations centered at different frequencies.

  DFT discretely estimates a single spectral component of an input signal that is equal to one element of the Fourier transform.

More specifically, if {x _i } is a discrete sequence of complex values corresponding to N samples of one complex signal, the DFT of channel k of {x _i } is defined as follows: .

Or in a compact form,

  here,

Thus, the DFT can be viewed as a linear combination of samples x _i , where the weight W, also called “twiddle factor”, is an increment of k in increments of N phases in the complex domain. It is a different N-th root. For a “two-sided” spectrum k, both negative and positive integer values can be assumed (−N <k <N).

  In the well-known frequency shift theory, equation 6) above can also be interpreted as the average of a series of sinusoids with shifted frequencies. Actually, the term 7) is a complex sine curve having a frequency of k / NT. product

Is to just the spectrum of x _i, shifted on the frequency axis backward by the size of the k / NT without changing the spectral shape itself of x _i. The average operation in the frequency domain has the following transfer function:

  Here, f is the frequency and N is the number of samples.

  Therefore, the transfer function of the DFT operator can be obtained by multiplying the spectrum of the “shifted frequency” signal by the average transfer function 8) as follows:

  Here, T is the sampling period, f is the frequency of the sine wave signal, N is the number of samples used in the DFT, and k is the DFT expressed as 1 / (N · T) as the unit number as described above. Indicates the discrete position of the center frequency.

  Referring now to FIG. 2, frequency response curves 50a, 50b of three different DFT operators centered on three consecutive frequency bins corresponding to n = -1, n = 0 and n = 1, respectively. 50c can be identified.

  Thus, each DFT response has a center peak 502 and a second maximum point 504 at f = k / NT. The response of the DFT operator is exactly zero at a distance away from the center peak frequency by each multiple of the DFT bin width 1 / NT.

  Absolute value extraction is used to extract the real non-negative amplitude value of the complex DFT output.

  A possible approach to constructing a DFT frequency estimator is associated with the following quantity evaluation.

Here, DFT _D and DFT _U represent operators | DFT (x, -1) | and | DFT (x, + 1) |, that is, DFTs corresponding to the curves 50a and 50c in FIG. It becomes as follows.

  In the discriminator of Equation 10), the frequency is estimated using the amplitude difference between two DFTs having k = + 1 and k = -1. In this case, this difference is normalized using the sum of the amplitudes of the two DFTs.

  3 and 4 illustrate the theoretical response and relative gain of the discriminator of equation 10). The advantage of this discriminator is that the response is strictly linear, i.e. the gain is constant, in the frequency range of f = -1 / (NT) to f = 1 / (NT).

However, a major limitation of this approach is that in the frequency region near f = 0, both DFTs tend to be zero, making the differential noise dominant. This problem is amplified by the fact that because of the shape of the response R _x , the normalization factor also tends to be zero. Therefore, the result is mathematically indefinite near f = 0. FIG. 5 shows the same response as FIG. 3, but with the simulated random noise added to the input signal. It is clear that this discriminator shows essentially random results for frequencies close to f = 0.

  Thus, the discriminator of equation 10) has an unstable point at the center of its frequency range and therefore cannot be used for most practical applications. A technique for preventing this problem is to add a DFT 50c corresponding to k = 0 to the normalization coefficient as follows.

  FIG. 6 shows the discriminator response of Equation 13), and FIG. 7 shows the response of simulated noise added thereto. Here, the noise margin is satisfactory, but the discriminator has essentially no gain for frequencies very close to f = 0. In some applications, this fact can be detrimental, especially in the FFL loop of FIG.

  In one aspect of the invention, the frequency discriminator includes an evaluation of two 1/2 bin discrete Fourier transforms (HDFT) at different frequencies, in which case the 1/2 bin DFT is defined by equation 13 above. The index k takes a half integer value.

  In particular,

It is.

  However, when the equation defining the twiddle factor W is examined, it becomes as follows.

  Therefore, HDFT is calculated by the same method as normal DFT, but the twiddle factor W takes a value assuming that the order of Fourier transform is 2N, not N.

The transfer function of HDFT (in absolute value) is still given by equation 9). The transfer function of the HDFT operator has a maximum value at the frequency at the half integer value with respect to the sampling frequency of the sample set (x _i ), whereas the DFT operator defined above has the maximum value at the integer frequency value. You can see that it has a value.

  More specifically, it is defined as follows.

  And the equation of the frequency discriminator is as follows.

  However, the peak frequency is centered at a half integer value of the 1 / NT DFT bin width.

The frequency extraction operators H _D and H _U relate to linearly combining the weights or twiddle factors that are N 1 complex roots in 2N different 1 2N power roots with the sample x _i. .

  For example, FIG. 8 illustrates an HDFT response curve 55a corresponding to k = −1 / 2 and an HDFT response curve 55c corresponding to k = 1/2. The response curve 55b corresponding to k = 0 is the same as the response curve 50b in FIG.

  Compared to the DFT curve of FIG. 2, it can be seen that curves 55a and 55c are not simultaneously zero for f = 0. This makes it possible to construct a 1/2 bin frequency discriminator having the response and gain illustrated in FIGS.

Advantageously, the 1/2 bin discriminator of the present invention has a denominator of equation 17) that does not tend to be zero for f = 0, so that f _D = −½NT to f _U = ½NT. It exhibits a linear response along the entire operating range and is stable over the entire operating range. FIG. 11 illustrates the operation of a 1/2 bin discriminator according to the present invention in the presence of a standard distribution of noise.

The mathematical expression for “½ bin DFT” can also be derived from the special features of the FFT algorithm. The complex FFT takes a vector of N samples of the signal and calculates N spectral lines at i / NT for 0 ≦ i <N. Sometimes, in order to artificially increase the resolution of the calculated spectrum, N zeros are added to the end of the input sample vector to calculate an FFT of 2N points. This operation generates N new spectral lines at (2i + 1) / 2NT for 0 ≦ i <N, located exactly in the center of the 2N FFT frequency bins. Considering that the FFT algorithm is only an optimization and reconstruction of a collection of N DFTs, the 1N to 2N-1 (negative frequency) spectral lines of the FFT at 2N points are equivalent to that DFT. By substituting, the 1/2 bin DFT equation can be derived. The DFT at 2N points for k = 1 to k = 2N−1 is as follows:

  However, considering that the last N points of the input vector are zero:

  This last equation is exactly the same as the previously derived ½ bin DFT equation.

Thus, in one aspect of the invention, the frequency discriminator corresponds to at least two discrete spectral components of the input signal, preferably two frequencies f _D and f _U that are located symmetrically above and below the zero frequency. Calculating two spectral components.

Each spectral component is extracted by an operator H _D or H _U with a maximum response for the desired spectral components f _D and f _U. Of course, this response is decreased with respect to different frequencies, for intermediate frequency between f _D and f _U, decreases in a manner that the response does not become zero. In particular, the responses of H _D and H _U do not reach zero at the midpoint of f = 0.

For this characteristic, the discriminator of the present invention, extracts the frequency error signal obtained by the calculation step of dividing the difference between the absolute value of the output of the HDFT _D and HDFT _U the sum of the absolute value of the output of the HDFT _D and HDFT _U can do.

Both the sum and difference of the absolute values of the outputs of HDFT _D and HDFT _U are not allowed to be zero at any point in the range between f _D and f _U , so the discrimination obtained The device works well even when considering the unavoidable effects of noise, and its value is linear between f _D and f _U.

By using the above-mentioned HDFT operator, the frequencies f _D and f _U of HDFT _D and HDFT _U are f _D = −1 / 2NT and f _U = 1 / 2NT, that is, sampled at the T sampling rate. When the sequence of N input digital data {x _i } is divided into natural binnig, it is located at the center of the half integer value.

In a preferred embodiment, the operators HDFT _D and HDFT _U have the form represented by equation 17) above. However, the operators HDFT _D and HDFT _U can also be obtained from different mathematical operators for extracting the frequency components of the input signal, according to the present invention, depending on the situation required.

  The 1/2 bin discriminator described above, despite its clear advantages, still has the limitation of having unstable points at frequencies outside the frequency range, such as ± 1.5, ± 2.5, etc. In particular, when the noise is high, FLLs that use such discriminators can lock onto these spurious frequencies.

  An approach to prevent this problem is to have an upper operator that has a transfer function peak at frequencies above and below the reference frequency (here, conventionally zero frequency) and does not exhibit zero or discontinuity in the operating frequency range. And making a frequency discriminator based on the operator below.

Although it is possible to define such upper and lower operators using both DFT _U and DFT _D defined in equation 11) and HDFT _U and HDFT _D defined in equation 16), A non-unique approach is represented by operators C _D and C _U having the transfer function illustrated in FIG.

As desired, the synthetic operator C _D below has a maximum value of the transfer function at the frequency f _D below 0 and the indicated reference frequency in the graph of FIG. 15. The upper compositing operator C _U has the maximum value on the contrary at the frequency f _U above the reference frequency.

C _D and C _U is, throughout their range, it can be seen that no both zero and discontinuities. Therefore, C _D and C _U, it is seen that can be used to make a frequency discriminator which operates well in both inside and outside the lock range.

Since C _D <C _U for x <0, while C _D > C _U for x> 0, a simple example of a discriminator according to the present invention is defined by the following discriminator function: Is done.

By including the proportional term DFT _center in the denominator as defined by equation 12), the performance of the above discriminator can be further improved in both bandwidth and linearity. An improved discriminator according to the invention is, for example, the following symmetric 1/2 bin DFT discriminator.

Here, the coefficient k ₁ is a normalization coefficient that can be arbitrarily selected in principle, and k ₂ is selected to have an optimum value that compromises between the bandwidth and linearity of the response. Good performance and center gain, equal to other discriminators, for example

And k ₂ = 3/2.

  FIGS. 13 and 14 represent the transfer function and gain of the discriminator HSDFT (x) of equation 22), respectively. It can be seen that the gain is well constant within the expanded frequency range between -0.75 and 0.75. In this case, the lock range of the discriminator based on HSDFT (x) is noticeably wider than any of the other discriminators described above.

  Another advantageous characteristic is that the zero point is not discontinuous or unstable even in the entire frequency spectrum, even beyond the lock range. That is, the transfer function 109d of the HSDFT (x) of the discriminator according to the present invention is changed from the transfer function 190b of the “cross” discriminator, the transfer function 190a of the “crossSign” discriminator, and “ It becomes more apparent by examining FIG. 16 compared to the transfer function 190c of the “arctan” discriminator. This comparison also shows that the bandwidth of the transfer function 190d is wider than that known.

  Thanks to these properties of the invention, it is possible to realize a frequency control device that focuses on the target frequency faster and more accurately than devices based on known discriminators. Furthermore, it is possible to realize a frequency control device that does not have a spurious lock state.

  The present invention also includes a receiver, particularly a GPS receiver, for the wireless positioning system described herein in connection with FIG.

  The receiver has a receive antenna 20 adapted to a specific radio signal from the source of the radio location system. In the GPS system, the source is an on-orbit GPS space vehicle that emits a 1575.42 MHz radiolocation signal. The signal received by this antenna is amplified by the low noise amplifier 30 before being supplied to the carrier removal stage 49, and down-converted to an intermediate frequency signal (IF signal) by the conversion unit 35. Other methods for processing RF signals, including, for example, analog to digital conversion, are well known in the art and are included in the present invention.

  The IF signal is then fed first to the correlation processor, whose function is to despread the signals received from each SV and produce them on a locally generated copy of the pseudo-random ranging code specific to each SV. For example, in the case of a GPS receiver, the role of the correlation processor is the demodulation and tracking of the GPS ranging signal for coarse acquisition (C / A). To perform such an arrangement, the correlation processor has an array of tracking modules 38, each of which is specialized for capturing and tracking a particular SV, for example.

  In the following, various functions of the tracking module 38 will be described with reference to FIG. However, it should be understood that this description is given by way of example only and should not be construed as limiting the invention. In particular, the various components and modules described herein are understood as functional terms and do not necessarily correspond to physical circuit components. In particular, some functions are provided by software modules that are executed by one or more digital processors.

  Here, for the sake of clarity, the various tracking modules 38 will be described quite independently and in parallel, but some characteristics or sources may be shared between the tracking modules, depending on the circumstances required. .

  Each tracking module has a conventional local NCO 40 for generating a local oscillator signal and a carrier removal with a 90 ° phase shifter 41 for generating a replica of the quadrature component of the local oscillator signal. A stage 49 is included. In a possible variation, the 90 ° phase shift can also be done with an external pre-circuit. The radio input signal is multiplied by the in-phase and quadrature signals of the local oscillator in multipliers 44 and 42, respectively, to generate an in-phase baseband signal I and a quadrature baseband signal Q. In tracking mode, the frequency or phase of the NCO 40 is locked to the carrier frequency or phase of the SV being tracked.

  Each tracking module 38 also has a local gold sequence pseudo-random code generator 50 to generate a local copy of the C / A code corresponding to a particular GPS space vehicle. The gold series pseudo-random code can be generated, for example, internally by a tapped shift register, similarly extracted from a pre-loaded table, or generated by other methods.

  The gold series code generator 50 includes a C / A clock that is independently numerically controlled, and the frequency thereof is set to generate a C / A code at a chip rate of 1.023 MHz. Two components of the in-phase component (I) and the quadrature component (Q) of the IF signal are multiplied by the local C / A code by the multipliers 52 and 54. While tracking, the local C / A code needs to be temporally locked to the C / A code received from the SV. The local carrier frequency and phase must be locked to the carrier frequency and phase of the received signal in order to correct for the Doppler shift of the SV signal and the frequency drift and bias of the local oscillator.

  The correlation data for the in-phase signal and the quadrature signal can be regarded as the real part and the imaginary part of the complex signal. In an ideal frequency lock state, the NCO 40 frequency and the carrier frequency are the same, and the signal produced at the input of the discriminator 70 is a pure baseband signal with a fundamental frequency of zero. During tracking, the discriminator module 70 generates a frequency error signal 65 that is used to drive the NCO 40 of the carrier removal stage in the feedback loop to lock to the frequency of the received signal.

In the present invention, the discriminator module 70 described herein with reference to FIG. 18 comprises a frequency discriminator based on the aforementioned HDFT or preferably HSDFT. More particularly, the discriminator module 70 according to the present invention corresponds to at least two discrete spectral components of the input signal, preferably two frequencies f _D and f _U which are symmetrically located above and below the zero frequency. Extract one spectral component.

Each spectral component is extracted by the frequency extracting means 702 or 704 having the maximum response to the desired spectral components f _D and f _U , respectively. This response is naturally reduced for different frequencies, but the response is reduced in such a way that it is not zero for any intermediate frequency between f _D and f _U. In particular, the response of the frequency extraction means 702 and 704 does not become zero at the midpoint of f = 0. In this way, stable operation of the discriminator module 70 within the locking range is ensured.

  More preferably, the frequency extraction means 702 and 704 have a frequency response that is never zero at any frequency. In this way, the control loop including discriminator module 70 and NCO 40 has no spurious lock points other than the desired point.

Because of this property, the discriminator of the present invention preferably calculates the difference between the absolute values of the outputs of 702 and 704 by dividing the difference by the sum of the absolute values of the outputs of the frequency extraction means 702 and 704. By doing so, the frequency error signal obtained by the comparison means 706 arranged for normalization can be extracted. In another embodiment, the frequency extraction means will often when executed by the microprocessor, and a software module having a code for calculating the values H _D and H _U. In an implementation variant corresponding to the discriminator of equation 22) above, an auxiliary extraction means not shown is used to extract the term HDFT _centre .

For simplicity, in this example, the frequency extraction means 702 and 704 are illustrated as separate elements, but the present invention provides a single that sequentially extracts the required two spectral components f _D and f _U. It can also be understood as having frequency extraction means.

By using the HDFT and HSDFT operators described above, the frequencies of f _D and f _U are f _D = −1 / 2NT and f _U = 1 / 2NT, ie, N samples sampled at the T sampling rate. With respect to the segmentation of the sequence of input digital data {x _i } into natural bins, it will be located at the center of the half integer value.

In a preferred embodiment, the frequency extraction means 702 and 704 implement the operators H _D and H _U that have the form defined by Equation 17) above. However, in this invention, in order to extract the frequency component of the input signal, operators H _D and H _U, depending on the circumstances necessary, it can also be obtained from different mathematical operators.

  The frequency discriminator of the present invention is based on a variation of the DFT transform that replaces the normal twiddle factor with a twiddle factor for the DFT at twice the actual number of sampling points. Such a modified DFT allows for a 1/2 bin frequency discriminator with only a slight increase in computational load. Two DFTs shifted by ½ bin with respect to zero frequency provide a linear response of discrimination and good immunity to noise. By using both the 1/2 bin term and the full bin term in the discriminator function, the frequency estimation and dynamics can be further improved, and HSDFT is an example of this approach. The discriminator of the present invention is particularly useful in FLL for tracking signals in GPS receivers.

  Depending on the situation, the discriminator module 70 can be implemented as a dedicated electronic digital circuit or as a microcontroller device programmed to carry out the steps of the method according to the invention. The invention also includes software code that can be loaded into the program memory of a computer device for performing the steps described above when executing the program.

Block diagram of a known FLL including a frequency discriminator Absolute value graph of transfer functions of three DFT operations centered on three adjacent frequency bins Response graph of frequency discriminator based on two of the DFTs of FIG. 2 in an ideal condition without noise Gain graph of the discriminator of FIG. Operation graph of the discriminator of FIG. 3 in the presence of a standard distribution of noise. Frequency discriminator response graph based on the three DFTs of FIG. 2 in an ideal condition without noise Operation graph of the frequency discriminator of FIG. 6 in the presence of a standard distribution of noise. Absolute value graph of three DFT operations when shifted by 1/2 frequency bin Response graph of frequency discriminator based on two DFTs at both ends of FIG. Gain graph of the discriminator of FIG. Operation graph of the frequency discriminator of FIG. 9 in the presence of a standard distribution of noise. Absolute value graph of 5 DFT operations when shifted by 1/2 frequency bin Response graph of frequency discriminator based on DFT in FIG. Gain graph of frequency discriminator based on DFT in FIG. FIG. 14 is a graph of the transfer function of two shifted synthesized operators used in the discriminator of FIG. Comparison graph of the response of the frequency discriminator according to the invention and the prior art frequency discriminator Schematic diagram of a receiver / tracker module of a GPS receiver based on one aspect of the present invention. Schematic diagram of the frequency discriminator module deployed in the receiver of FIG.

Explanation of symbols

10 Receiver for GPS positioning system (GPS receiver)
20 receiving antenna 30 low noise amplifier 35 conversion unit 38 tracking module 40 local oscillator (NCO)
41 90 ° phase shifter 42 multiplier 43 input signal 44 multiplier 45 mixer 46 local oscillator 47 frequency discriminator 48 filter 49 carrier removal stage 50 local gold sequence pseudo random code generator 50a, 50b, 50c DFT operator frequency Response curve 502 Center peak of DFT response 504 Second maximum point of DFT response 52 Multiplier 54 Multiplier 55a, 55b, 55c Frequency response curve of HDFT operator 65 Frequency error signal 70 Discriminator module 702, 704 Frequency extraction means 706 Comparison Means 155a, 155b, 155c, 155d, 155e Absolute value curve 190a of HDFT operator Response curve 190b of sine dot cross type discriminator Response curve 190c of cross type discriminator Response curve 190d of arctangent type discriminator Quadrature component of the phase component Q IF signal synthesis operator C _U above the synthetic operator IF intermediate frequency I IF signal having a frequency C _D below the frequency f _U above the response curve f _D below the discriminator by

Claims (9)

A method for obtaining a frequency difference between a frequency of an input signal composed of N consecutive samples and a reference frequency,
Applying a discrete number of spectral component extraction operators to the corresponding sample to extract corresponding spectral components of the input signal;
For the spectral component in question, a lower amplitude operator with a maximum transfer function at the lower frequency, and a higher frequency above the reference frequency and higher than this lower frequency. Mathematically combining an upper amplitude operator having a maximum transfer function at
Obtaining a frequency difference of interest from the values of the lower amplitude operator and the upper amplitude operator;
In a method comprising:
A method wherein the response of these lower and upper amplitude operators does not indicate a zero or discontinuity within the operating frequency range.   The method of claim 1, wherein the responses of the lower and upper operators do not indicate zeros or discontinuities at any frequency.   The method of claim 1, wherein the upper frequency and the lower frequency are located symmetrically around a reference frequency.   Each of the lower and upper operators corresponds to a DFT operation obtained by a linear combination of samples having N different N-th complex N-th roots as weighting factors, and 2N different 1-complex 2N The method according to claim 1, wherein the method is a combination with a ½ bin DFT operation obtained by a linear combination of samples using a root as a weighting factor.   The method of claim 1, wherein the frequency difference is obtained by a single value of the lower and upper operators.   The method of claim 1, wherein the frequency difference is obtained by the lower and upper operators and is obtained from values of one or more DFT operators and 1/2 operators. A frequency discriminator device having an input for receiving an input signal and a frequency discriminator means for generating an output signal in response to a difference between the fundamental frequency of the input signal and a reference frequency, the frequency discriminator means comprising: It has frequency extraction means for extracting the discrete spectral components of the input signal at the lower frequency and the upper frequency, and these lower frequency and upper frequency are located above and below the reference frequency, respectively. In a frequency discriminator device in which the response of the discriminator device is determined by discrete spectral components at the lower and upper frequencies of the input signal,
A frequency discriminator device characterized in that the response of the frequency extraction means does not become zero for any frequency within the operating frequency range.   The input signal consists of N number of consecutive samples, and for each of these samples, each of the frequency extraction means is a sample of samples with N different complex N-th roots as weighting factors. In the form of executing a combination of a DFT operation obtained by a linear combination and a 1/2 bin DFT operation obtained by a linear combination of samples having 2N different complex 2N power roots as weighting factors. 8. A frequency discriminator device according to claim 7 configured to be operable. A GPS receiver having a frequency discriminator stage for generating an output signal that depends on the difference between the fundamental frequency and the reference frequency of the input signal of the frequency discriminator means, the frequency discriminator stage being below the input signal Frequency extraction means for extracting discrete spectral components at the upper frequency and the upper frequency, the upper frequency and the lower frequency are respectively located above and below the reference frequency, respectively, and the response of the frequency discriminator device In a GPS receiver, where is determined by discrete spectral components at the lower and upper frequencies of the input signal,
A GPS receiver characterized in that the response of the frequency extraction means does not become zero at any frequency within the operating frequency range.

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